here is a link to the API reference for geometry utilities that do not rely on a geometry service.i don't have any relevant experience with using geometry services hosted by PostGIS, but i would assume that you might have a hard time using Esri JavaScript API method calls if you aren't using a geometry service hosted by ArcGIS Server. that being said, tasks.arcgisonline.com includes a geometry service that i believe is allowed to be referenced in production applications.
what exactly do you mean by this? are you saying the work needs to be done entirely clientside?
if not, have you already seen the documentation related to the REST geometry service (which includes a union, intersect and difference operation)?our JavaScript API simplifies making calls to run these operations from a client web application, but you still have to make asynchronous calls to ArcGIS Server
(in the browser)
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